Heron's formula finds the area of a triangle with side lengths a, b, and c and s is the "half perimeter", s= (a+ b+ c)/2. s is also a length so all four are units of length (feet, yards, meters, centimeters, etc.) Then, of course all four of s, s- a, s- b, and s- c have units of length also. That means that s(s- a)(s- b)(s- c) has units of "length to the fourth power".
But area always has units of "length square" (square feet, square yards, square meters, square centimeters, etc.). That is why the square root is needed:
\(\displaystyle A= \sqrt{s(s- a)(s- b)(s- c)}\).